C₁₁×#33728 #14610921

order	2816
nilpotency class	4
isoclinism	isoclinic class of #2218
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₁ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₁₁×#33728

Subgroups

	subgroup	G/H
center	C₂×C₄×C₁₁	C₂×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₁₁
socle	C₂²×C₁₁	C₂²×D₈
prime radical	C₂³×C₁₁	C₂×D₈
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₁ ◁ C₂×C₄²×C₁₁ ◁ C₂×C₄×C₈×C₁₁ ◁ G

482 conjugacy classes of subgroups; only the 270 normal subgroups are shown.

normal subgroups only

This group has 482 conjugacy classes of subgroups — too many to draw. Only its 270 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

minimal degree	μ(G) = 51
transitive degree	μ_t(G) = 1408

A minimal faithful permutation representation — 4 generators on 51 points:

(1,2,3,4,5,6,7,8,9,10,11)(12,13,15,17)(14,18,19,16)(20,21)(22,31)(23,28)(24,38)(25,40)(26,30)(27,35)(29,33)(32,44)(34,45)(36,50)(37,43)(39,51)(41,47)(42,49)(46,48);(12,14,15,19)(13,16,17,18)(22,32)(27,41)(31,44)(34,36)(35,47)(42,46)(45,50)(48,49);(20,22,33,48,25,36,39,47,26,32,37,49,23,34,24,35)(21,27,38,45,28,42,43,44,30,41,51,50,40,46,29,31);(20,23,26,25)(21,28,30,40)(22,34,32,36)(24,37,39,33)(27,42,41,46)(29,38,43,51)(31,45,44,50)(35,49,47,48)

Conjugacy classes & character table

572 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 26716);